Despite the importance of both criteria, intelligibility appears to be much more difficult to circumscribe than accuracy.
Indeed, in the statistical learning literature, the generalization ability of classifiers has been formally characterized
through the prisms of learnability [1]}, [2]}, uniform convergence [3]}, and algorithmic stability [4]}, [5]}.
By contrast, the term “intelligibility” holds no agreed upon meaning,
since it depends on various desiderata for clarifying the classifier behavior in some practical situations [6]}.
Yet, different forms of intelligibility can be formalized, by focusing on the classifier ability to properly answer questions.
Such forms of intelligibility are reflected by explanation and verification queries introduced so far in the XAI literature.
Notably, a classifier should be equipped with explanation facilities including, for example,
the ability to identify few relevant features which together are sufficient for predicting the label of a data instance.
Furthermore, the classifier should be amenable to inspection, especially when the user has some expectations about
the behavior of the classifier, and she is interested in checking whether the classifier complies to those expectations.
For instance, in a loan classification problem, if a loan is granted to an applicant who does not have a high income,
then loan should not be denied when the income increases, provided that the other features are unchanged.
This expectation can be formalized using a verification query that checks the monotonic behavior
of the classifier on the feature related to the applicant's income.
